Introduction
As a mathematics professor at a Christian college, I am often asked to consider how I integrate my faith with the work I do as a mathematician and a mathematics teacher. I find this ‘integration of faith and learning’ to be a challenging and often frustrating task. Upon reflection over the past few months, I have realized that the source of my frustration is not my inability to put these two aspects of my life together, but rather the difficulty I have in separating them out in the first place. The word ‘integration’ implies a blending together of things which are initially distinct; yet, I have always viewed my mathematical study as an important part of my growth as a Christian, as I search for God’s truth and beauty.
In my own experience, I cannot recall a time when I considered my study of mathematics to be anything other than an integral part of my personal Christian faith. Perhaps this is true in my life for several reasons. I became a Christian at a young age, long before I began seriously studying mathematics. My parents and my Presbyterian church family encouraged me to approach issues in faith from a rational perspective, emphasizing reason and respect for God’s power and creativity. As an analytic thinker by nature, I found this approach to religion appealing. When I attended Wheaton College for my undergraduate education and chose a mathematics major, it seemed natural for me to view a mathematician’s search for quantitative and logical truth as part of a larger search for philosophical and religious truth and beauty. My professors seemed to hold this view as well, and they often expressed an attitude of worship in their work. For instance, to a Christian mathematician, the frequent occurrence of the irrational number pi in studies of geometry or of ø, the golden ratio, in the natural world, or the intricacies of the Mandelbrot set, may be as awe-inspiring and convincing of God’s existence as a clear, star-filled sky is to the casual observer. Mathematics supplies the foundation for many of the applied and social sciences, and Christian mathematicians who explore these foundational ideas consider their work to be good stewardship of their talents and gifts, as valuable to society and the church as the work of a doctor or social worker.
As a teacher, having taught in both secular and Christian environments, I find that students come to mathematics classrooms with a variety of experiences and attitudes, and many of them do not share my inclination to value mathematical thought and ideas as part of Christian stewardship and worship through discovery. On the contrary, some students who struggle with mathematical concepts dislike the subject so much that they have a difficult time identifying anything in mathematics beyond basic arithmetic which is useful or relevant to their lives. Certainly, a substantial number of students, particularly those in general education courses, do not enter a mathematics course expecting to find examples of beauty and eloquence that they might look for in their art, literature, or Bible courses. Teaching at a Christian college, I have the opportunity and responsibility to share my Christian perspective of mathematics with students in my courses, as a meaningful aspect of material we cover in the course. Integrating this perspective into my teaching so that the connections between mathematics and Christianity are clear even to skeptical students requires prior planning and organization, and I value this integration project as a format for organizing my thoughts and materials to distribute to students.
As an undergraduate student at Wheaton College, I particularly remember learning that many of the mathematicians whose works form the foundation of mathematics also studied theology and in some cases wrote extensively about their religious beliefs. Examples of these mathematicians include Johannes Kepler, Isaac Newton, and Rene DesCartes. I was impressed as a student to realize that so many of those who made great contributions to mathematical thinking were great religious thinkers, and they were drawn to worship their Creator through their work. I was fortunate to learn about the biographies of these men and women in mathematics history and philosophy courses I took as a part of my major. Students in general education courses or service courses for other majors are likely to hear about the mathematical contributions of a few of these people, in the context of a particular course, but they are less likely to learn about the mathematicians’ faith, unless course and textbook material is supplemented by additional summaries. Therefore, for my project, I intend to compile a collection of short, one page summaries, describing both the mathematical and religious contributions of mathematicians whose work is central to the courses I teach, including Introduction to Mathematics, Elementary Functions (Precalculus), Calculus, and Geometry. In future semesters, when I teach these courses, I will distribute these summaries to students at appropriate times when we are studying the work of a particular mathematician. My goal is for students to see some of the connections other mathematicians have made between their mathematical studies and their faith, in addition to the connections which I point out regularly in class. I will encourage students, particularly mathematics majors, to keep these summaries and use them as a starting point for their own future research. During this spring semester (1998), I will distribute all of the summaries to students in my Senior Mathematics Seminar, a capstone course in which issues of faith and philosophy are discussed.
I intend for this project to eventually become part of a larger Integration of Faith and Learning project, required by full time faculty at Messiah College. In this larger project, I plan to discuss in more depth my views of mathematical work as stewardship of God’s resources and discovery of His works in creation, as well as how I integrate these ideas into the courses I teach. I also anticipate that the supplementary course material developed for this project will be expanded, as I have the opportunity to teach seminar courses and discuss with students their reactions and thoughts about the process of integrating faith and mathematics.
Biographies of Mathematics and Faith
Rene DesCartes
Rene DesCartes was born in 1596 in the small French town of La Haye, two hundred miles from Paris. His father was a provincial judge, and DesCartes was raised to become a gentleman. He attended a prestigious elementary school known as the Jesuit College of La Felche. Since his health was delicate, DesCartes was pampered as a student; he was allowed to lie in bed as late as he pleased, and he spent a great deal of time in bed, thinking and writing. One of DesCartes’ friends at school, Marin Mersenne, sparked his serious interest in mathematics. Years later, DesCartes turned to mathematics as a model for discovering truth in philosophy and science.
DesCartes’ search for truth began with a rejection of all accepted doctrines and dogmas. In his words, "I thought that I ought to reject as absolutely false all opinions in regard to which I could suppose the least ground of doubt, in order to ascertain whether after that there remained anything in my belief that was wholly indubitable."1 Beginning with the hypothesis "Je pense, donc je suis" ("I think, therefore I am"), DesCartes used the reasoning of mathematics to build up systems of truth in philosophy, science, and religion. His most significant work, Discours de la Methode pour bien conduire sa Raison et chercher la Vrit dans les Sciences (Discourse on the Method of Rightly Conducting the Reason in the Search for Truth in the Sciences) was published in 1637, and it outlined DesCartes’ method of study.
In one of the appendices to Discourse, La Geometrie, DesCartes introduces the field of analytic geometry, a combination of the methods of algebra and geometry which has proven to be his most powerful and significant contribution to the field of mathematics. Tradition maintains that DesCartes first thought of analytic geometry as he lay in bed watching a fly crawl on the ceiling and trying to identify its location. In La Geometrie, DesCartes also introduced much of the mathematical notation in use today, including the common use of x, y, and z as variables, and modern exponential notation.
DesCartes was reluctant to publish many of his works, because he considered himself a devout Roman Catholic and the Church was threatened at that time by his ideas about the formation of the solar system, and the position of the sun rather than the earth at the center of the universe. In Meditations, published in 1641, DesCartes discusses his philosophical conclusions about the nature of God, the soul, and eternal truths. The ideas set forth in Meditations have been debated by both orthodox Christians and philosophers since they were published, but certainly DesCartes’ writings indicate that he sought to apply the same reasoning he employed in mathematics to questions of Christian faith. This is reflected in the following excerpt from Discourse:
I have noticed certain laws which God has established in nature, and of which he has established such notions in our souls, that having reflected on them sufficiently it is impossible for us to doubt that they are obeyed with exactness in everything which exists or which happens in the world.2
References:
Burton, David M. The History of Mathematics: An Introduction, 2nd ed., Wm. C. Brown Publishers, Dubuque, IA, 1991.
Re, Jonathan. DesCartes, Pica Press, New York, 1974.
1 as cited in Burton, p. 330.
2 as cited in Re, p. 144.
Johannes Kepler
Johannes Kepler was born in 1571 in a village in southern Germany. His parents were poor and unstable in many ways; his father was a drunken soldier and his mother was accused of witchcraft later in life. Johannes contracted smallpox when he was four years old, which crippled his hands, weakened his eyesight, and left him an outcast among his peers. He was fortunate to receive a good education which originally prepared him for service in the Lutheran ministry. One of his professors, however, awakened his interest in astronomy, particularly in a Copernican view of the solar system. This heliocentric model maintained that the earth is a planet revolving around the sun, rather than placing the earth at the center of the universe. This theory was such a radical departure from the accepted Ptolemaic theory that it was considered heretical. With this view, Kepler was considered unfit for the ministry. In 1594, Kepler began teaching mathematics at a Protestant seminary in Southern Austria, where he remained for four years. He later worked with the astronomer Tycho Brahe, who had collected many precise observations about the movements of the planets. Kepler analyzed this information, and it formed the basis of his laws of planetary motion.
Much of Kepler’s work in mathematics and astronomy was motivated by his search for simple mathematical laws to describe the motions of the planetary system. His painstaking analysis of the observation of the planets led him to the conclusion that the planet Mars orbits the sun in an elliptical orbit, not the circular orbit others had assumed. In fact, all of the planets orbit the sun in an elliptical path, and this is Kepler’s first law of planetary motion. The second law is that the radius vector joining a planet to the sun sweeps out equal areas in equal periods of time. In establishing this law, Kepler divided the sector swept out by a planet into thin sectors whose area could be approximated by a triangle. This approach was a precursor to the ‘Riemann sums’ of integral calculus. Kepler used similar methods to approximate the volume of partially full wine barrels.
Although Kepler was not a theologian or minister by occupation, understanding the mind of God was very important to him, and he worshiped his Creator through his discoveries. In one letter, Kepler wrote "For a long time, I wanted to become a theologian; for a long time I was restless. Now, however, behold how through my effort God is being celebrated through astronomy."1 At the conclusion of one of his published works, Harmonice mundi, he wrote "Praise Him, ye celestial harmonies, praise Him, ye judges of the harmonies revealed, and thou my soul, praise the Lord Thy Creator, as long as I shall be!"2 In the design of the universe, Kepler discovered amazing harmony, and his prayer was "If I have been allured into rashness by the wonderful beauty of Thy works, or if I have loved my own glory among men, while I am advancing in work destined for Thy glory, be gentle and merciful and pardon me; and finally deign graciously to effect that these demonstrations give way to Thy glory and the salvation of souls and nowhere be an obstacle to that."3
References:
Gingerich, Owen. The Eye of Heaven, American Institute of Physics, 1993.
Simmons, George F. Calculus Gems: Brief Lives and Memorable Mathematics, McGraw-Hill, New York, 1992.
Quotations from Kepler’s writings are taken from:
Johannes Kepler Gesammelte Werke (JKGW), Munich, 1937, as cited in The Eye of Heaven, Owen Gingerich.
1 letter from Kepler to Maestlin, 1595, JKGW, v. 13, p. 40.
2 Harmonice mundi, JKGW, v. 6, p. 368.
3 Harmonice mundi, JKGW, v. 6, p. 363.
Gottfried Leibniz
Gottfried Wilhelm Leibniz was born in Leipzig, Germany in 1646. His father died when Gottfried was only 6 years old. As a child, Gottfried’s studies were rather undirected and, as a precocious student, he read a variety of books, mastering both Latin and Greek by the time he was a teenager. According to Leibniz himself, "I began to think when I was very young; and before I was fifteen I used to go for long walks by myself in the woods, comparing and contrasting the principles of Aristotle with those of Democritus."1 At the University in Leipzig, Leibniz received a traditional education, with an emphasis on Lutheran doctrine. After graduation, he continued his education in both legal studies and philosophy and eventually secured a teaching position at Leipzig. Throughout his education, Leibniz valued mathematics as a language of reasoning which gives men and women the tools and methods necessary for solving all types of problems.
Leibniz’s interest in mathematics intensified once he met the mathematician Christiaan Huygens in Paris in 1672. Leibniz began to talk with other mathematicians and to share his own work with them. Among his contributions was a mechanical calculator which performed both multiplication and division. Leibniz was also one of the first to develop the system of binary arithmetic. Ars Combinatoria, published in 1666, summarized Leibniz’s work developing the theory of combinations and permutations. In this work, Leibniz discusses the language of reasoning that mathematics provides, as a "basic alphabet of human thoughts"2.
Leibniz’s most significant contribution to mathematics was his development of infinitesimal calculus, which he published in 1684. Unknown to Leibniz at the time, Isaac Newton had discovered the field of calculus nine years earlier, but Newton had not published his work. The simultaneous independent discovery of calculus by both Newton and Leibniz sparked a great deal of suspicion and controversy between the two mathematicians which led to academic tension between England and France for years to come.
Leibniz applied the deductive reasoning of mathematics to many fields of study, including science, logic, political issues, and even civil engineering. He considered himself a Christian, and published work dealing with the essence of God, the creation of the universe, and the problem of evil. His book Theodicy, or "Vindication of the Justice of God", was published in 1710. At a time in history when rational thought and religious faith often seemed to be incompatible, Leibniz provided a valuable contribution to both academic and religious thought. According to author George Simmons: "[Leibniz] struggled for years to penetrate the mysteries of nature and God by the use of reason alone - by constructing a great metaphysical system that explains all things by the a priori method of deducing necessary consequences from a few self-evident principles."3
References:
Burton, David M. The History of Mathematics: An Introduction, 2nd ed., Wm. C. Brown Publishers, Dubuque, IA, 1991.
Ross, G. MacDonald. Leibniz, Oxford University Press, New York, 1984.
Simmons, George F. Calculus Gems: Brief Lives and Memorable Mathematics, McGraw-Hill, New York, 1992.
1 as cited in Burton, p. 367.
2 as cited in Burton, p. 367.
3 Simmons, p. 149.
Isaac Newton
Isaac Newton was born on Christmas Day, 1642 in Woolsthorpe, England. Newton’s father died before he was born and his mother married again while Newton was young, leaving Isaac with his grandmother and a maternal uncle, who raised him. Newton entered Trinity College, part of Cambridge University, in 1661. He remained at Trinity, studying mathematics and chemistry, until 1665, when an outbreak of the plague closed the university and Newton returned to his home in the country. He remained home for two years, from age 22 to 24, and during this time, he spend much time alone in study and completed a tremendous amount of work, making many discoveries in mathematics, astronomy, and physics. It was during this time that Newton first began to develop the foundations of calculus, although he did not publish his work. He also wrote the binomial theorem during this period. In 1669, Newton returned to Cambridge as a professor and remained there for 27 years. He continued to contribute greatly to the fields of mathematics and science, although he was rather secretive about his discoveries and reluctant to publish.
In the 1680s, Newton began writing his most well known work, the Philosophiae Naturalis Principia Mathematica, commonly referred to as the Principia. In this work, Newton established the foundations of several branches of science, including theoretical mechanics, fluid dynamics, and wave motion. Later in the same decade, a French mathematician, Gottfried Leibniz, began publishing his own results about the foundations of calculus, which were very similar to Newton’s work on the subject. When Newton learned of these publications, he, as well as many of his English colleagues in mathematics, became suspicious of Leibniz and accused him of plagiarizing Newton’s work. These accusations sparked a lively "Newton-Leibniz" controversy between England and France which continued for many years. In 1696, Newton left Cambridge for a position in London as Warden of the Mint. In this position, he continued his work in science and mathematics and published Opticks in 1704 . Isaac Newton’s contributions to fields of science are at least as significant as his contributions to mathematics.
Later in his life, Newton turned to the study of theology, writing works such as Observations upon the Prophecies of Daniel and the Apocalypse of St. John which was published in 1733, six years after his death. Throughout his lifetime, Newton viewed his scientific work as a way of discerning order and design in the universe. In a letter written in 1692, Newton wrote of his Principia, "When I wrote my treatise about our System I had an eye upon such Principles as might work with considering men for the belief of a Deity, and nothing can rejoice me more than to find it useful for that purpose."1
Isaac Newton was a man of rare scientific genius, but toward the end of his life, he reflected to his nephew: "I do not know what I may appear to the world; but to myself I seem to have been only like a boy, playing on the sea shore, and diverting myself, in now and then finding a smoother pebble or a prettier shell than ordinary, whilst the great ocean of truth lay all undiscovered before me."2
References:
Manuel, Frank E. A Portrait of Isaac Newton, Harvard University Press, Cambridge, Mass., 1968.
Simmons, George F. Calculus Gems: Brief Lives and Memorable Mathematics, McGraw-Hill, New York, 1992.
1 Correspondence, Isaac Newton, v. III, p. 233 (Newton to Bentley), 1963. (as cited in Manuel, F. E.)
2 Anecdotes, observations, and characters of Books and Men, London, 1820, p. 54. (as cited in Manuel, F. E.)
Florence Nightingale
Florence Nightingale was born in 1820 in England, the daughter of wealthy English parents who provided her with servants, education, and all the means of entering proper English society. Rejecting her expected role in this society, Florence felt called at a young age to make a difference in the lives of the poor, needy, and ill. At the time, British hospitals were often dark, filthy institutions which bred disease and death. In her search to make a difference, Florence traveled to other countries and observed the conditions of sanitation, personnel, diet, buildings, and methods of care in their health-care facilities. She took detailed notes on her observations, organized her information, and drew conclusions about improvements which needed to be made in the British system. She returned to London and became manager of the London Womens’ Hospital.
The changes Florence made in the procedures at the hospital caught the attention of the medical community. When British forces battling Russian troops at the Crimea requested nurses to care for the wounded in 1854, Florence was name Superintendent of the Female Nursing Establishment of the English General Hospitals in Turkey. Within six months, as a result of her work, a new hospital was built and the death rate fell from 42% to 22%. Eventually, Florence contracted one of the fevers which plagued her patients; this illness almost took her life and weakened her for the rest of her years. Returning to England as a national heroine, she continued her work improving civilian hospitals, publishing a textbook for nursing students (Notes on Nursing, 1860) and gathering data to present to health officials. In 1907, Florence Nightingale was the first woman to receive the Order of Merit from the British government. By this time, she had lost her sight and was weakened physically. She died in August 1910.
One of the keys to Florence Nightingale’s success in improving health conditions was that she took copious notes on aspects of health care and organized this information in order to analyze it, draw conclusions, and make appropriate changes. In her notes, she used graphical displays of information similar to what are now known as pie charts. She was recognized for her skill in interpreting large amounts of data and standardizing information such as the classification of disease so that different hospitals could compare their findings. In all of her work, she sought to make the valuable connection between statistical information and the practice of health care.
Florence Nightingale considered her lifetime work to be a divine calling; at age 17, she wrote in her diary, "On Feb. 7, 1837, God spoke to me and called me to His service." When she heard God’s voice, she did not know what work He was calling her to do, but she trusted Him to guide her life, rather than trusting society’s expectations for a women at the time. Practices in health care in the nineteenth century improved dramatically as a result of Florence Nightingale’s faithfulness to her work.
References:
Cooney, Miriam P., ed. Celebrating Women in Mathematics and Science, National Council of Teachers of Mathematics, Reston, VA, 1996.
Kendall, Maurice, and R. L. Plackett, eds. Studies in the History of Statistics and Probability, Vol. II, chapter 19.
Blaise Pascal
Blaise Pascal was born in June, 1623, in Auvergne, France. His mother died when Blaise was 3 years old, leaving the care and education of Blaise and his two sisters to his father, Etienne. Etienne Pascal directed Blaise’s education, and, for some reason, he felt that his son should not study mathematics until he reached age 15. Despite Blaise’s great curiosity about the subject, all mathematics textbooks were kept locked up and out of his reach. Finally, when he was 12, Blaise began to draw figures on the floor and discover geometry for himself. Popular legend reports that he was able to reconstruct all of Euclid’s 32 propositions in the Elements, there on his playroom floor. After seeing this, his father lifted the ‘mathematics ban’ and encouraged his son’s talent. Etienne Pascal was fortunate to be a contemporary of mathematicians such as Ren Descartes and Girard DesArgues, and Blaise was able to listen to the conversations of these men at a young age.
Blaise Pascal’s first published work, Essai sur les coniques ("Essays on Conic Sections") was written when Pascal was only 16 years old. He was truly a precocious young man, particularly in the area of geometry. Pascal’s Theorem, which states that if a hexagon is inscribed in a conic section, the three points of intersections of opposite sides are collinear, is one of the most important theorems in projective geometry. Pascal was also a scientist and inventor; his contributions include the barometer, a calculating machine, and the wrist watch. In addition, he is known for the foundational work he did in developing the theory of mathematical probability, which includes the famous arithmetic triangle of binomial coefficients, better known as "Pascal’s triangle". Although Pascal was not the first to describe and analyze this triangle, it bears his name, perhaps because of his published work, Triangle Arithmtique.
Blaise Pascal was a Christian, and he spent much of his life struggling to balance his mathematical genius with his religious devotion. Because of several factors, including the religious culture at the time, family influence, and Pascal’s own mental and physical health, he felt that mathematical study was harmful to his soul. Therefore, Pascal went through periods of his life when he did not allow himself to do any scientific work, followed by periods of great productivity, when his mathematical genius ‘burst through’, almost against his will. His writings in the area of religion include Provincial Letters, a series of short letters attacking the teaching of the Jesuits, and Penses, a collection of Pascal’s thoughts which he meant to be a defense of Christianity. This work, although disjointed and not completed before Pascal’s death, is considered one of the classics of French literature. Tragically, Pascal died in France at the young age of 39.
References:
Bell, E.T. Men of Mathematics: The Lives and Achievements of the Great Mathematicians from Zeno to Poincar, Simon & Schuster, New York, 1986.
Burton, David M. The History of Mathematics: An Introduction, 2nd ed., Wm. C. Brown Publishers, Dubuque, IA, 1991.
Simmons, George F. Calculus Gems: Brief Lives and Memorable Mathematics, McGraw-Hill, New York, 1992.
